Maximum Likelihood Symbol Research Articles

Coordinate Interleaved High-Dimensional OFDM With Index Modulation

In this letter, we propose a novel multicarrier transmission scheme named as coordinate interleaved high-dimensional orthogonal frequency division multiplexing with index modulation (CI-HD-OFDM-IM). In each subblock of the proposed scheme, two HD symbols with the optimal rotation angles are combined by coordinate interleaving technique to obtain an additional diversity gain and improve bit error performance. The single HD symbol maximum likelihood (ML) detection is exploited in the receiver. The average bit error probability (ABEP) of the CI-HD-OFDM-IM in the frequency selective Rayleigh fading environment is derived. Simulation results show that the proposed scheme has significantly better error performance than the reference systems, and the derived ABEP is very accurate.

C-RAN-Type Cluster-Head-Driven UAV Relaying With Recursive Maximum Minimum Distance

In this letter, a Cloud Radio Access Network-type cluster-head-driven uplink model for multiple-antenna Unmanned Aerial Vehicles (UAV) relaying schemes is presented, which enables joint Maximum Likelihood symbol detection in the UAV cluster-head and the selection of UAV sources to communicate with each other aided by UAV-based relays. A relay selection technique, named Cluster-Head-Driven Best-Link (CHD-Best-Link), which employs cluster-head buffers and physical-layer network coding, is devised. A recursive maximum minimum distance relay selection strategy that exploits time-correlated channels and equips the CHD-Best-Link scheme is also developed. Simulations illustrate that CHD-Best-Link has superior average delay and bit error rate performances to that of previous schemes.

QOSTBC coded MIMO system with reduced complexity and optimised decoding for rank deficient channels

In multiple-input multiple-output (MIMO) systems, rank deficient channels are the most common and key areas of research. In these channels, the number of transmit antennas (M Tx) is higher than receive antennas (M Rx) and subsequently the unknown variables are more than the number of equations. In such situations, the conventional sphere decoder (SD) fails due to the presence of zero diagonal elements in Cholesky decomposition. This study analyses the quasi-orthogonal space-time block code (QOSTBC) of symbol rate-2 for M Tx = 4 with modified double-layer SD detection to overcome rank deficiency problem. The first half of transmitted symbols is detected using two partially dependent SDs with optimised search radii. The remaining half is detected by employing single symbol maximum likelihood detection. Simulation and analytical results indicate that the proposed detection scheme reduces bit error rate and complexity compared to existing techniques.

McLeish Distribution: Performance of Digital Communications Over Additive White McLeish Noise (AWMN) Channels

The objective of this article is to propose and statistically validate a more general additive non-Gaussian noise distribution, which we term McLeish distribution, whose random nature can model different impulsive noise environments commonly encountered in practice and provides a robust alternative to Gaussian noise distribution. In particular, for the first time in the literature, we establish the laws of McLeish distribution and therefrom derive the laws of the sum of McLeish distributions by obtaining closed-form expressions for their probability density function (PDF), cumulative distribution function (CDF), complementary CDF (C2DF), moment-generating function (MGF) and higher-order moments. Further, for certain problems related to the envelope of complex random signals, we extend McLeish distribution to complex McLeish distribution and thereby propose circularly/elliptically symmetric (CS/ES) complex McLeish distributions with closed-form PDF, CDF, MGF and higher-order moments. For generalization of one-dimensional distribution to multi-dimensional distribution, we develop and propose both multivariate McLeish distribution and multivariate complex CS/ES (CCS/CES) McLeish distribution with analytically tractable and closed-form PDF, CDF, C2DF and MGF. In addition to the proposed McLeish distribution framework and for its practical illustration, we theoretically investigate and prove the existence of McLeish distribution as additive noise in communication systems. Accordingly, we introduce additive white McLeish noise (AWMN) channels. For coherent/non-coherent signaling over AWMN channels, we propose novel expressions for maximum a priori (MAP) and maximum likelihood (ML) symbol decisions and thereby obtain closed-form expressions for both bit error rate (BER) of binary modulation schemes and symbol error rate (SER) of various M-ary modulation schemes. Further, we verify the validity and accuracy of our novel BER/SER expressions with some selected numerical examples and some computer-based simulations.

Lossless Dimension Reduction for Integer Least Squares With Application to Sphere Decoding

Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE point has a vital difference at low SNRs. By exploiting the information provided by the MMSE method, we prove the existence of a lossless size reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless size reduction-aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.

A Novel Receiver Design and Maximum-Likelihood Detection for Distributed MIMO Systems in Presence of Distributed Frequency Offsets and Timing Offsets

In distributed multi-input multi-output (MIMO) systems, antennas may not be able to utilize common oscillators at the transmitter side or the receiver side. Consequently, there are multiple carrier frequency offsets (CFOs) and multiple timing offsets (TOs) due to distributed antennas that may significantly degrade the system performance if not properly addressed. In this paper, we analyze the effect of multiple CFOs and multiple TOs on receiver signal energy at the front end of each receive antenna pulse matched filter output in a distributed MIMO system. We then propose a novel receiver design for distributed MIMO systems that can accommodate multiple CFOs and multiple TOs. The proposed receiver structure utilizes a bank of pulse matched filters at each receive antenna where each filter accommodates one CFO specifically. Each filter output is then sampled at the symbol rate, with sampling timing selected according to the corresponding TO, followed by an information symbol detector. For the proposed receiver configuration, we derive the maximum-likelihood (ML) symbol detector for both space-time block coded and uncoded distributed MIMO systems. In addition, we design sub-optimal detectors and show that under certain conditions, the sub-optimal detectors perform close to the ML-optimal detector with significantly lower complexities. Extensive simulation studies illustrate our theoretical development for distributed MIMO systems with various transceiver configurations and channel conditions. The simulation results indicate that the proposed receiver structure together with the ML detection offers significant performance gains compared to the current state of the art.

One symbol training receiver for the SPAD-based UVLC system.

For the long distance single photon avalanche diode (SPAD)-based underwater visible light communication (UVLC) system, the multiple-symbol union detection scheme is presented. However, an error floor curve of the bit-to-error ratio (BER) occurs and cannot vanish even though the transmitted power approaches infinity. In this paper, to solve the problems of error floor and channel estimation in the long distance SPAD-based UVLC system, we propose the one training symbol maximum likelihood (ML) detection receiver. First, we add one training symbol in the head of each frame to eliminate the error floor and ensure the reliable blind estimation of the long distance UVLC channel. Meanwhile, the training ML detection (TMLD) receiver is developed. And then, to improve the system performance, a training modified (TM) quasi-ML receiver with Anscombe root transformation is proposed. Compared to the traditional mean detection scheme of the SPAD receiver, the simulation results show that the proposed TM quasi-ML and TMLD schemes significantly improve the error-rate performance.

SBL-Based Joint Sparse Channel Estimation and Maximum Likelihood Symbol Detection in OSTBC MIMO-OFDM Systems

This paper presents sparse Bayesian learning (SBL)-based schemes for approximately sparse channel estimation in an orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) wireless system. The parameterized prior-based SBL framework is employed to present a pilot scheme for an ill-posed OSTBC MIMO-OFDM channel estimation scenario. Maximum likelihood symbol detection (MLSD) has been incorporated in the expectation-maximization framework for SBL-based channel estimation. This has led to the development of a novel scheme for joint approximately sparse channel estimation and symbol detection. The proposed scheme performs SBL-based channel estimation in the E-step followed by a modified ML decision metric-based symbol detection in the M-step. Bayesian Cramer–Rao bounds are obtained for the genie minimum mean-squared error estimators corresponding to the SBL schemes. Closed-form bit error probability expressions are derived for the MLSD in the presence of SBL-based channel estimation errors. Simulation results are presented towards the end to validate the theoretical bounds and illustrate the performance of the proposed techniques.

Symbol Synchronization for Diffusion-Based Molecular Communications.

Symbol synchronization refers to the estimation of the start of a symbol interval and is needed for reliable detection. In this paper, we develop several symbol synchronization schemes for molecular communication (MC) systems where we consider some practical challenges, which have not been addressed in the literature yet. In particular, we take into account that in MC systems, the transmitter may not be equipped with an internal clock and may not be able to emit molecules with a fixed release frequency. Such restrictions hold for practical nanotransmitters, e.g., modified cells, where the lengths of the symbol intervals may vary due to the inherent randomness in the availability of food and energy for molecule generation, the process for molecule production, and the release process. To address this issue, we develop two synchronization-detection frameworks which both employ two types of molecule. In the first framework, one type of molecule is used for symbol synchronization and the other one is used for data detection, whereas in the second framework, both types of molecule are used for joint symbol synchronization and data detection. For both frameworks, we first derive the optimal maximum likelihood (ML) symbol synchronization schemes as performance upper bounds. Since ML synchronization entails high complexity, for each framework, we also propose three low-complexity suboptimal schemes, namely a linear filter-based scheme, a peak observation-based scheme, and a threshold-trigger scheme, which are suitable for MC systems with limited computational capabilities. Furthermore, we study the relative complexity and the constraints associated with the proposed schemes and the impact of the insertion and deletion errors that arise due to imperfect synchronization. Our simulation results reveal the effectiveness of the proposed synchronization schemes and suggest that the end-to-end performance of MC systems significantly depends on the accuracy of the symbol synchronization.

Suboptimal maximum likelihood detection of on-off keying for a wireless optical communication system.

This paper investigates a detection scheme without channel state information for wireless optical communication systems. Employing conventional on-off keying signals, we supposed that conditional probability density function P(r|0) is much bigger than P(r|1) when r<0. Under this assumption, the suboptimal maximum likelihood scheme is obtained by utilizing the probability density function without channel information. Theoretical analysis shows the performance of the proposed scheme is close to the maximum likelihood symbol-by-symbol detection. Compared with the maximum likelihood symbol by symbol detection, Monte Carlo simulations show that the performance of the proposed scheme is about 0.62 dB loss for a gamma-gamma channel with a Rytov variance of 1 at the signal-to-noise ratio of 2 dB, but the efficient algorithm makes the real-time implementation of detection based on maximum likelihood feasible. Besides, the experiment is set up under 2 Gbps, and the experimental results match well with that of the theory and simulation.

ML Symbol Detection for MIMO Systems in the Presence of Channel Estimation Errors

In wireless communication, the multiple-input multiple-output (MIMO) system is a well-known approach to improve the reliability as well as the data rate. In MIMO systems, channel state information (CSI) is typically required at the receiver to detect transmitted signals; however, in practical systems, the CSI is imperfect and contains errors, which affect the overall system performance. In this paper, we propose a novel maximum likelihood (ML) scheme for MIMO systems that is robust to the CSI errors. We apply an optimization method to estimate an instantaneous covariance matrix of the CSI errors in order to improve the detection performance. Furthermore, we propose the employment of the list sphere decoding (LSD) scheme to reduce the computational complexity, which is capable of efficiently finding a reduced set of the candidate symbol vectors for the computation of the covariance matrix of the CSI errors. An iterative detection scheme is also proposed to further improve the detection performance.

Iterative ML Symbol Detection without Timing and Phase Synchronization

This paper deals with maximum-likelihood (ML) detection of symbol sequence in the absence of synchronization information. A novel iterative scheme is proposed to obtain the ML estimates of the symbols without an estimation of synchronization parameters. Instead of the optimal sampling point recovery and explicit carrier phase compensation, the detection of symbols employs the direct calculation of the matched filter output, eliminating the need for a separate synchronizer. The detection problem is treated as ML estimation from incomplete data, which is solved by means of an iterative scheme based on the expectation-maximization algorithm. The proposed scheme is compared with conventional non-data-aided and iterative ML synchronizers. Accordingly, the simulation results indicate that the proposed detector enables improvements on both the bit error rate and convergence property.

Complexity Reduction in Joint Decoding of Block Coded Signals in Overloaded MIMO-OFDM System

This paper presents a low complexity joint decoding scheme of block coded signals in an overloaded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. In previous literature, a joint maximum likelihood decoding scheme of block coded signals has been evaluated through theoretical analysis. The diversity gain with block coding prevents the performance degradation induced by signal multiplexing. However, the computational complexity of the joint decoding scheme increases exponentially with the number of multiplexed signal streams. Thus, this paper proposes a two step joint decoding scheme for block coded signals. The first step of the proposed scheme calculates metrics to reduce the number of the candidate codewords using decoding based on joint maximum likelihood symbol detection. The second step of the proposed scheme carries out joint decoding on the reduced candidate codewords. It is shown that the proposed scheme reduces the complexity by about 1/174 for 4 signal stream transmission.

Hybrid Tree Search Algorithms for Detection in Spatial Multiplexing Systems

Hybrid tree search algorithms are described for maximum-likelihood symbol detection in spatial multiplexing (SM) systems. Essentially, the search tree is iteratively expanded in breadth-first (BF) manner until the probability that the current most likely path is correct exceeds the specified threshold, at which point, the depth-first (DF) stage is initiated to traverse the rest of the tree. In contrast with the sphere decoding (SD) algorithm, which starts off with the DF search, the proposed algorithms use the BF stage to enhance the accuracy of the initial DF search direction by exploiting the diversity inherent in the SM scheme. Simulation results demonstrate that, with a moderate increase in the memory requirement, the proposed algorithms achieve a significantly lower complexity than the SD algorithm in many scenarios.

New design of no-zero-entry single symbol ML decodable STBCs based on group precoding

In multiple-input multiple-output (MIMO) systems, space–time block codes (STBCs) from orthogonal designs (ODs) and coordinate interleaved orthogonal designs (CIOD) have been attracting wider attention due to their amenability for fast (single symbol) maximum-likelihood (ML) decoding, and full-rate with full-rank over quasi-static fading channels. However, most of these codes, for transmitting antennas more than 4, have large number of zero entries in their codeword matrix. Due to the zero entries in the design, the transmitting antennas need to be switched on and off imposing severe hardware constraints. To solve this problem, we propose a method to generate a new class of no-zero-entry single symbol maximum likelihood decodable STBCs (NZESSDCs), which is based on coordinate interleaving and group precoding technique. The ability of the proposed group precoding based NZESSDCs (called G-NZESSDCs) on single symbol ML Decoding and full diversity are analyzed and derived. The performance evaluation is accomplished by numerical simulation and is compared with recently reported NZESSDCs (called C-NZESSDCs). Compared with C-NZESSDCs, the proposed G-NZESSDCs have same bit-error-rate (BER) performance and better peak-to-average ratio (PAPR) performance.

Low Complexity Demapping Algorithms for Multilevel Codes

In order to reduce the computational complexity of maximum-likelihood symbol estimation (MLSE) demapping of multilevel codes which is based on block partitioning and which produces soft input for a multistage decoding (MSD) process, three different demapping algorithms are proposed. It is theoretically proven that the proposed algorithms can reduce exponentially increasing computational complexity of the MLSE demapping algorithm to a constant complexity (neglecting comparisons). It is shown by extensive simulations for AWGN and Rayleigh fading channels that the proposed low complexity demapping algorithms can achieve near MLSE performance.

On the performance evaluation of an LTE SFBC system with Wiener channel estimation in frequency-selective channels

The uncoded performance of an Alamouti space-frequency block code operating in a frequency-selective channel is studied in the presence of channel estimation errors. The Alamouti Maximum Likelihood (ML) symbol detector with linear combining is considered at the receiver. Imperfect channel estimates are provided by a realistic as well as robust Wiener interpolator. A closed-form expression of the uncoded error probabilities of a space-frequency block code employing an Alamouti with linear combining is derived. Our analysis is conducted in the framework of a Long-Term Evolution air interface. The impact of channel estimation errors on the uncoded performance of the system is evaluated as a function of key system parameters, such as the anticipated power delay profile at the channel estimator, the actual, i.e. true, power delay profile, the pilot spacing and the Wiener filter length. The role of partial knowledge of the channel statistics is investigated as well. Finally, we derive a lower bound from our closed-form expression and calculate the bit error outage of the linear Alamouti combiner in presence of log-normal fading signal-to-noise ratio (SNR).

Timing Synchronization for Cooperative Communications with Detect and Forward Relaying

A non-data-aided near maximum likelihood (NDA-NML) symbol timing estimator is presented, which is applied to a cooperative communication system with a source, relay and destination. A Cramer rao bound (CRB) for the estimator for asymptotically low signal-to-noise (SNR) ratio case is derived. The timing complexity of the NDA-NML estimator is derived and compared with the correlation based data-aided maximum likelihood (DA-ML) estimator. It is demonstrated that the complexity of the NDA-NML estimator is much less than that of correlation based DA-ML estimator. The bit-error-rate (BER) performance of this system operating in a detect-and-forward (DAF) mode is studied where the channel state information (CSI) is available at the receiver and the symbol timings are estimated independently for each channel. SNR combining (SNRC) and equal ratio combining (ERC) methods are considered. It is found that timing estimation error has a significant effect on BER performance. It is also found that for large timing error the benefit of cooperative diversity could vanish. It is demonstrated that significant gains can be made with both combining methods with cooperation and timing estimation, where the gains are the same for both estimators.

ML Symbol Detection Based on the Shortest Path Algorithm for MIMO Systems

This paper presents a new maximum likelihood (ML) symbol detection algorithm for multiple-input multiple-output (MIMO) systems. To achieve the ML performance with low complexity, we search the integer points corresponding to symbol vectors in increasing order of the distance from the unconstrained least-squares solution. For each integer point, we test if it is the ML solution, and continue the integer point search until one of searched points is determined to be the ML solution. We present an efficient iterative search strategy, which is based on the shortest path algorithm for a graph. The simulation results show that the proposed algorithm has the lower complexity compared to the sphere decoding for channel matrices having low condition numbers. For further complexity reduction, we propose to use scaling, lattice-reduction, and regularization techniques. By applying these techniques, the computational complexity of proposed algorithm is reduced significantly when the channel matrix has a high condition number.

Maximum Likelihood (ML) Symbol Timing Recovery (STR) Techniques for Reconfigurable PAM and QAM Modems

A fast symbol timing recovery (STR) scheme suitable for flexible-symbol-rate, burst-mode M-ary QAM (M-QAM) and PAM (M-PAM) demodulators used in broadband communications is proposed. The maximum- likelihood (ML) estimation is used to derive a feed-forward STR strategy to achieve fast and accurate derivation of the optimum timing instant with a very short training preamble for applications requiring short packet transmission. In addition, the signal sample at the optimum timing instant is reproduced by interpolation. Analysis to derive the ML-based timing estimation algorithm and STR structure is presented. Analytical models are developed to evaluate the effects of imperfect interpolation and channel additive white Gaussian noise (AWGN) on the timing estimation performance. The derived expressions can be used for optimum interpolation filter design and selection of key parameters to achieve the required mean squared timing error. Simulation results are in good agreement with the analytical prediction.